# ISEE Lower Level Math : Geometry

## Example Questions

### Example Question #11 : Rectangles

A rectangle has a length of 10 feet and a width of 1 foot. What is the area of the rectangle?

Explanation:

The area of a rectangle is calculated by multiplying the length by the width.

Given that the length is 10 feet and that the width is 1 foot we can multiply to find the final area:

### Example Question #33 : Quadrilaterals

What is the area of a rectangle with a width of 6 inches and a length of 7 inches?

Explanation:

The area of a rectangle is equal to the length multiplied by the width. Since the width is 6 inches and the length is 7 inches, the area is equal to 6 times 7.

The area is 42 square inches.

### Example Question #34 : Quadrilaterals

If a rectangle has a perimeter of 40, a width of 4, and a length of 4x, what is the value of x?

Explanation:

The perimeter of a rectangle is equal to

Thus, .

Subtract 8 from both sides:

Divide both sides by 8:

### Example Question #31 : Quadrilaterals

A rectangle has a perimeter of 30. One of its sides has a length of 6. What is its area?

Explanation:

If the rectangle has one side that is , we know that two of them must be that size. Therefore, we know that it looks something like this:

If the perimeter is 30, you know that the following equation holds:

This means that the other two sides can be found by solving for :

The area of a rectangle is equal to its base times its height:

### Example Question #21 : How To Find The Area Of A Rectangle

A rectangle has two sides that are each . Its other sides are twice this length. What is the area of the rectangle?

Explanation:

If one side is , the doubled side must be . Therefore, the rectangle looks like this:

The area of a rectangle is equal to its base times its height:

### Example Question #31 : Quadrilaterals

What is the area of the following rectangle?

Explanation:

The area of a rectangle is defined as the base multiplied by its height. Therefore, for this rectangle:

### Example Question #31 : Plane Geometry

One side of a rectangle has a length of 10. What is the area of this rectangle if it has a perimeter of 120?

Explanation:

Based on what we were told, our rectangle looks like this:

We know, therefore, that there is  or  remaining for the other two sides. This means that they are . So, our rectangle ultimately looks like this:

The area of a rectangle is its base times its height. Therefore, the area is:

### Example Question #32 : Quadrilaterals

A rectangle has a width of  and a length of . Find the area of the rectangle.

Explanation:

To find the area of a rectangle apply the formula:

This problem provides the measurements for both the width and length of the rectangle.

Thus, the solution is:

### Example Question #21 : How To Find The Area Of A Rectangle

A rectangle has a width of  and a perimeter measurement of . Find the area of the rectangle.

Not enough information is provided.

Explanation:

In this problem you are given the width and perimeter of the rectangle. However, to solve for the area of the rectangle you must first find the length of the rectangle. To do so, work backwards using the formula:

Now that you know the width and length of the rectangle, apply the area formula:

### Example Question #51 : Geometry

Find the area of the rectangle shown above.

Explanation:

To find the area of a rectangle apply the formula:

The image provides the measurements for both the width and length of the rectangle.

Thus, the solution is:

Tip for mental math: Since you are multiplying  times a multiple of ten, you can think of these factors as:

and then tack on one zero to the product because the orginal factors have a total of one zero--which equals a product of .